﻿1120 Mr. S. J. Barnett on Electric Fields due to the 

 The magnetic moment of the sphere is 



so that, with proper attention to signs, 

 Qi=f c [»M]. 



Outside the sphere the magnetic field is that o£ a point 

 doublet of moment M at the centre of the sphere. The 

 vector potential is thus 



a=-[mv*] ; 



so that 



^=i-{A«) = -i([MV^],) = - c -(vi.[«M]) ) 



which is the potential of an electric point doublet with 

 moment 



Q-i[«M] 



at the centre of the sphere. 



The outward radial component of the intensity at the 



surface of the sphere due to the doublet of moment Q is 



20 



— ^cos S. Thus the surface density of the part of the charges 



terminating the outer field is 



Q a 2lv a 



<7 2 — t, 5 COS V= 4 r— ,COS = ^0-1. 



lira 6 6 cr 



The total charges upon the upper and lower hemispheres 

 terminating the outer field are thus 



2ira 2 Iv 

 and the moment of these charges is 



Q 2 =2Qi. 



The total surface density upon the two hemispheres is thus 



<T = (7 Y + (T 2 = -Y COS U, 



